Divisors of 27225: All 27 Factors

Divisors (Factors) Calculator

Use the calculator above to find all divisors (also called factors) of any positive integer up to 4,782,969. Beyond the divisor list, this tool also shows divisor pairs, the sum and count of divisors, prime factorization, and number properties (prime, perfect square, perfect number).

All Divisors of 27225

The number 27225 has 27 divisors:

1,  3,  5,  9,  11,  15,  25,  33,  45,  55,  75,  99,  121,  165,  225,  275,  363,  495,  605,  825,  1089,  1815,  2475,  3025,  5445,  9075,  27225

Divisor Pairs of 27225

Each pair multiplies to 27225:

Note: the last pair has identical factors (165 × 165) because 27225 is a perfect square.

Number of Divisors

The number 27225 has 27 divisors, written as τ(27225) = 27 in number theory.

⚡ Notice: 27225 has an odd number of divisors — this means 27225 is a perfect square (√27225 = 165).

Sum of Divisors

σ(27225) = 1 + 3 + 5 + 9 + 11 + 15 + 25 + 33 + 45 + 55 + 75 + 99 + 121 + 165 + 225 + 275 + 363 + 495 + 605 + 825 + 1089 + 1815 + 2475 + 3025 + 5445 + 9075 + 27225 = 53599

Prime Factorization of 27225

See the full prime factorization calculator →

Properties of 27225

• 27225 is composite.
• 27225 is a perfect square (√27225 = 165).
• Number of divisors: 27.
• Sum of divisors: 53599.

Common Divisors with Another Number?

Looking for the divisors that 27225 shares with another number? Use our Greatest Common Factor (GCF) calculator — it finds all common divisors and the largest one.

Step-by-Step: How to Find the Divisors of 27225

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √27225 ≈ 165.00. If i divides 27225, then both i and 27225/i are divisors.

1. 1 divides 27225 (27225 ÷ 1 = 27225) → pair (1, 27225)
2. 3 divides 27225 (27225 ÷ 3 = 9075) → pair (3, 9075)
3. 5 divides 27225 (27225 ÷ 5 = 5445) → pair (5, 5445)
4. 9 divides 27225 (27225 ÷ 9 = 3025) → pair (9, 3025)
5. 11 divides 27225 (27225 ÷ 11 = 2475) → pair (11, 2475)
6. 15 divides 27225 (27225 ÷ 15 = 1815) → pair (15, 1815)
7. 25 divides 27225 (27225 ÷ 25 = 1089) → pair (25, 1089)
8. 33 divides 27225 (27225 ÷ 33 = 825) → pair (33, 825)
9. 45 divides 27225 (27225 ÷ 45 = 605) → pair (45, 605)
10. 55 divides 27225 (27225 ÷ 55 = 495) → pair (55, 495)
11. 75 divides 27225 (27225 ÷ 75 = 363) → pair (75, 363)
12. 99 divides 27225 (27225 ÷ 99 = 275) → pair (99, 275)
13. 121 divides 27225 (27225 ÷ 121 = 225) → pair (121, 225)
14. 165 divides 27225 (27225 ÷ 165 = 165) → pair (165, 165)
15. Collect all unique values: {1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 121, 165, 225, 275, 363, 495, 605, 825, 1089, 1815, 2475, 3025, 5445, 9075, 27225} — total 27 divisors.
16. Sum: 1 + 3 + 5 + 9 + 11 + 15 + 25 + 33 + 45 + 55 + 75 + 99 + 121 + 165 + 225 + 275 + 363 + 495 + 605 + 825 + 1089 + 1815 + 2475 + 3025 + 5445 + 9075 + 27225 = 53599.

Nearby Examples

Related Operations for 27225

• Multiples of a Number — "outward" complement of divisors
• 27225 Prime Factorization — decompose into prime building blocks
• Find GCF of 27225 and another number
• Find LCM of 27225 and another number
• Is 27225 a perfect square? (odd divisor count ⇔ yes)

See also our tables of divisors:

• Table of all divisors from 1 to 100
• Table of all divisors from 1 to 500
• Table of all divisors from 1 to 1,000
• Table of all divisors from 1 to 10,000

What Is a Divisor?

A divisor (also called a factor) of a positive integer n is any positive integer d such that n ÷ d has no remainder. In other words, d divides n evenly.

Every positive integer n has at least two divisors: 1 and n itself (with 1 being the trivial case of having only itself). Numbers with exactly 2 divisors are prime; numbers with 3 or more divisors are composite.

Why use this calculator? Beyond just listing divisors, this tool computes the sum σ(n), the count τ(n), prime factorization, divisor pairs (useful for visual learners and factoring problems), and detects whether n is a prime, a perfect square, or a perfect number.

References

• [1] Divisor (Wikipedia)
• [2] Divisor function (Wikipedia)
• [3] Divisor (Wolfram MathWorld)

Divisors Calculation Examples

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